Thanks, "new card offers" - are you referring "view all credit cards under cards tab"?The concept of NLL links has largely fallen by the wayside (with limited exceptions) because Amex has largely stopped issuing them this year.
The better way to think about it is, if you can get approved for a card without a pop-up, you will get the bonus. That includes a card you've had before.
One way of getting a bonus on a card you've had before is to check your Amex account often — they regularly target people for new card offers there, even for cards you've already had.